Problem: Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

* First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
* Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
* Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).



How many operations are necessary until the permutation is sorted?

Constraints

* 1 ≤ N ≤ 2×10^5
* (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Solution (in CPP):

Solution:
#include<cstdio>
#include<cstring>
#include<algorithm>
#define ll long long
using namespace std;
const int N=300010,P=1e9+7;
inline int read(){
	int x=0,f=0,c=getchar();
	for(;c>'9'||c<'0';f=c=='-',c=getchar());
	for(;c>='0'&&c<='9';c=getchar())
	x=(x<<1)+(x<<3)+c-'0';return f?-x:x;
}
int n,i,a[N],p[N],f[N],g[N];
int main(){
	//freopen("1.out","w",stdout);
	n=read();
	for(i=1;i<=n;i++)p[a[i]=read()]=i;
	f[n]=n;for(i=n-1;i;i--)
	if(!g[i+1]){
		if(p[i]>p[i+1])g[i]=1,f[i]=i+1;
		else g[i]=g[i+1],f[i]=f[i+1];
	}else{
		if(((p[i]<p[i+1])+(p[f[i+1]]<p[i])+(p[i+1]<p[f[i+1]]))==2)
		g[i]=g[i+1],f[i]=f[i+1];else g[i]=g[i+1]+1,f[i]=i+1;
	}printf("%d\n",g[1]);
	return 0;
}